What is d/(dr(t))((t)(t^{r(t)})) ?

The answer to d/(dr(t))((t)(t^{r(t)})) is t^{tr+2}ln(t)(rln(t)+(tr+2)/t)+t^{tr+1}

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d/(dr(t))((t)(t^{r(t)}))

\frac{d ^{2}}{d r d t} ((t) (t^{r (t)}))

t^{t r + 2} ln (t) (r ln (t) + \frac{t r + 2}{t}) + t^{t r + 1}

Solution steps

\frac{d ^{2}}{d r d t} ((t) (t^{r (t)}))

\frac{d}{d r} (t t^{r t}) = t^{t r + 2} ln (t)

= \frac{d}{d t} (t^{t r + 2} ln (t))

\frac{d}{d t} (t^{t r + 2} ln (t)) = t^{t r + 2} ln (t) (r ln (t) + \frac{t r + 2}{t}) + t^{t r + 1}

= t^{t r + 2} ln (t) (r ln (t) + \frac{t r + 2}{t}) + t^{t r + 1}

2 (x + 1)^{3} - 3 (x + 1)^{2} - 6

ab - 2 b + a y - 2 y

9 - 3 x

2 n^{2} - 0.7 n + 0.05

(64 x y)^{(\frac{1}{3})}

What is d/(dr(t))((t)(t^{r(t)})) ?
The answer to d/(dr(t))((t)(t^{r(t)})) is t^{tr+2}ln(t)(rln(t)+(tr+2)/t)+t^{tr+1}